Hopefully, swallowed my pride and gone after Gareth Bryne.

Morgase really didn't have many options here. She clearly wasn't going to roll over and let Gaebril or the Dragon Reborn take control of the nation while Elayne was the Creator only knows where on Aes Sedai business.

She also didn't have any allies. She broke alliances with all of her major supporters while under compulsion. She had no one to turn to inside Andor besides her own estates (clearly insufficient) or Gareth (too awkward). So she had to look outside Andor for allies, where there were also no good options. Tear and Cairhien were both controlled by the Dragon Reborn. Cairhien had also just finished a civil war, so it wasn't stable enough to look for allies anyway. Aes Sedai are too intermeshed with politics to be worthwhile. Murandy is divided. Ghealdan and Altara lack strong rulers. The Borderlanders aren't likely to care.

That leaves Amidicia and Illian, because apparently she didn't know how much power the Whitecloaks had and probably didn't know that Sammael controlled Illian. But Illian also lacks a single ruler, which is probably why she went for Amidicia.